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Compressive Sensing of Electrocardiogram Signals by Promoting Sparsity on the Second-Order Difference and by Using Dictionary Learning

机译:通过稀疏度在二阶差异和字典学习的心电图信号的压缩感知

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摘要

A new algorithm for the reconstruction of electrocardiogram (ECG) signals and a dictionary learning algorithm for the enhancement of its reconstruction performance for a class of signals are proposed. The signal reconstruction algorithm is based on minimizing the $ell _{p}$ pseudo-norm of the second-order difference, called as the $ell _{p}^{2d}$ pseudo-norm, of the signal. The optimization involved is carried out using a sequential conjugate-gradient algorithm. The dictionary learning algorithm uses an iterative procedure wherein a signal reconstruction and a dictionary update steps are repeated until a convergence criterion is satisfied. The signal reconstruction step is implemented by using the proposed signal reconstruction algorithm and the dictionary update step is implemented by using the linear least-squares method. Extensive simulation results demonstrate that the proposed algorithm yields improved reconstruction performance for temporally correlated ECG signals relative to the state-of-the-art $ell _{p}^{1d}$-regularized least-squares and Bayesian learning based algorithms. Also for a known class of signals, the reconstruction performance of the proposed algorithm can be improved by applying it in conjunction with a dictionary obtained using the proposed dictionary learning algorithm.
机译:提出了一种重构心电图信号的新算法和一种字典学习算法,以增强其对一类信号的重构性能。信号重构算法基于最小化信号的二阶差分的$ ell _ {p} $伪范数,称为$ ell _ {p} ^ {2d} $伪范数。所涉及的优化是使用顺序共轭梯度算法进行的。字典学习算法使用迭代过程,其中重复信号重建和字典更新步骤,直到满足收敛标准为止。通过使用所提出的信号重构算法来实现信号重构步骤,并且通过使用线性最小二乘法来实现字典更新步骤。大量的仿真结果表明,相对于最新的$ ell _ {p} ^ {1d} $正则化最小二乘和基于贝叶斯学习的算法,该算法对于时间相关的ECG信号具有更高的重建性能。同样对于已知的信号类别,可以通过将其与使用所提出的字典学习算法获得的字典一起应用来改善所提出算法的重建性能。

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